Issue 53

R. M. Reda et al., Frattura ed Integrità Strutturale, 53 (2020) 106-123; DOI: 10.3221/IGF-ESIS.53.09

F INITE ELEMENT FE MODEL

N

on-linear finite element FE using (ANSYS -Version 19.0) was performed to study the flexural behavior of RC beams strengthened with NSM technique [21]. First the present model was verified by comparing the model with the experimental results conducted by Reda et al. [8]. After validation, a parametric study was conducted. Elements Description ANSYS element library includes several elements which can be used to simulate the different types of materials [21]. In this research (SOLID65) was used to simulate concrete and epoxy adhesive, (SOLID65) has eight nodes with three degrees of freedom at each node – translations in the nodal x, y, and z directions. SOLID65 has the ability to crack in tension and crush in compression. The Willam and Warnke criterion was used to define the failure of concrete [15, 22], it is the available model in ANSYS material library to model concrete [15]. A (LINK180) element was used to model the steel reinforcement and NSM FRP bars. Two nodes are required for this element. Each node has three degrees of freedom, – translations in the nodal x, y, and z directions. The element is also capable of plastic deformation. An eight-node solid element (SOLID45) was used for the steel plates (Loading or supports) in the models. The element is defined with eight nodes having three degrees of freedom at each node-translations in the nodal x, y, and z directions [21].

10 15 20 25 30 35

Stress [MPa]

0 5

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004

Strain [mm mm^‐1]

(a) Concrete in compression (b) Concrete in tension [22]

(c) Steel (d) GFRP Figure 1: The stress strain curves used in model; concrete, steel and GFRP.

Materials Modeling Concrete, steel and GFRP stress strain curves used in model are shown in (Fig.1). (Fig. 1-a) defined the concrete as a material with a nonlinear behavior with a compressive strength, tensile strength, elastic modulus and Poisson’s ratio of 30 MPa and 2.9 MPa, 20 GPa and 0.2 respectively, open and closed crack shear coefficients were taken as 0.4 and 0.8 respectively, ( ε 0 is the strain at the ultimate compressive strength = 2 f c ’/ E c and; E c is the concrete elastic modulus [23]). (Fig. 1-d) shows the concrete behavior in tension simulated by smeared crack approach. Smeared crack approach has been adopted to define the concrete behavior in tension. The smeared crack approach was discussed previously by the authors [24]. The steel reinforcement was assumed to have an elastic-perfectly plastic response, (Fig. 1-c) shows the elastic-strain hardening behavior for the reinforcing steel bars with yield stress, elastic modulus and Poisson’s ratio of 420 MPa, 200 GPa and 0.3 respectively. The NSM GFRP bars were considered to be linear elastic up to failure, (Fig. 1-d), with tensile strength, elastic

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